Course projects

 ME697 - Computational Methods for Interface Dynamics.

Phase-field Modeling of dendritic solidification for different anisotropy configurations: In this project we solve a phase-field model of dendritic soldification with surface tension anisotropy by means of isogeometric analysis. Spatial discretization is performed using the Galerkin approach with C1-continuous quadratic splines. As a time-stepping scheme we use the generalized-α method, which provides second-order accuracy and A-stability. We study the time evolution of the phase-field variable and the temperature field during dendriticgrowth for different anisotropy configurations.

Keywords: solidification, phase-field, isogeometric analysis

Link to PDF: PDF

Animations of the results below: Top and bottom row show the phase field and the temperature field, respectively.

ME597 - Advanced Solid Mechanics.

Finite Strain Poroelasticity: In this course project, we perform a comprehensive study of poroelasticity taking the paper by W. Sun et al. as a reference. We derive the equations that describe the mechanical behavior of a fully-satured porous medium undergoing small deformations. We state and apply the mathematical operations needed to transform linear poroelasticity into large-deformation poroelasticity. Finally, we show examples and applications for a particular constitutive model.

Keywords: Poroelasticity, large deformations, anisotropy

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Displacement and pressure fields for a porohyperelastic material subjected to a source term in three different scenarios: a) no fiber reinforcement, b) one family of fibers at 45 degrees, c) two families of fibers at 45 degrees.

ECE563 - Programming Parallel Machines.

Parallel Numerical Solution of the 2D Heat Equation using OpenMP and MPI : In this course project, we discuss the numerical implementation and parallelization of the 2D transient heat equation using OpenMP and MPI. The spatial discretization of the partial differential equation is performed using a second-order, centered finite-difference scheme. For time discretization, we utilize a two-step explicit Runge-Kutta and an explicit Euler algorithm. The parallel performance of the codes is evaluated by conducting numerical experiments on the Scholar cluster available through Purdue RCAC and by analyzing speedup, efficiency and the Karp-Flatt metrics.

Keywords: PDEs, diffusion, parallel computing

Link to PDF: PDF

Temperature distribution at different times (top row). Steady state solution and error plot for transient problem using Jacobi method (bottom row).